The invention relates to a hydroformylation process using certain multidentate phosphite ligands. In particular, the ligands have heteroatom-containing substituents on the carbon attached to the ortho position of the terminal phenol group.
Phosphorus ligands are ubiquitous in catalysis and are used for a number of commercially important chemical transformations. Phosphorus ligands commonly encountered in catalysis include phosphines (A), and phosphites (B), shown below. In these representations, R can be virtually any organic group. Monophosphine and monophosphite ligands are compounds which contain a single phosphorus atom which serves as a donor to a metal. Bisphosphine, bisphosphite, and bis(phosphorus) ligands in general, contain two phosphorus donor atoms and normally form cyclic chelate structures with transition metals. 
There are several industrially important catalytic processes employing phosphorus ligands. For example, U.S. Pat. No. 5,910,600 to Urata, et al. discloses that bisphosphite compounds can be used as a constituting element of a homogeneous metal catalyst for various reactions such as hydrogenation, hydroformylation, hydrocyanation, hydrocarboxylation, hydroamidation, hydroesterification and aldol condensation.
Some of these catalytic processes are used in the commercial production of polymers, solvents, plasticizers and other commodity chemicals. Consequently, due to the extremely large worldwide chemical commodity market, even small incremental advances in yield or selectivity in any of these commercially important reactions are highly desirable. Furthermore, the discovery of certain ligands that may be useful for applications across a range of these commercially important reactions is also highly desirable not only for the commercial benefit, but also to enable consolidation and focusing of research and development efforts to a particular group of compounds.
One industrially important catalytic reaction using phosphorus ligands of particular importance is olefin hydroformylation. For example, U.S. Pat. No. 5,235,113 to Sato, et al. discloses a hydroformylation process in which an organic bidentate ligand containing two phosphorus atoms linked with an organic dihydroxyl bridging group is used in a homogeneous hydroformylation catalyst system. Hydroformylation processes involving organic bidentate ligands containing two trivalent phosphorus atoms, in which the two phosphorous atoms are linked with a 2,2xe2x80x2 dihydroxyl-1,1xe2x80x2-binaphthalene bridging group, are described in commonly assigned, copending application Ser. No. 60/087,151, filed May 29, 1998, and the patents and publications referenced therein.
Commonly assigned, published PCT Application W099/06357 discloses multidentate phosphite ligands with a structure having alkyl ether substituents on the carbon attached to the ortho position of the terminal phenol group for use in a liquid phase process for the hydrocyanation of diolefinic compounds.
It always remains desirable to provide even more effective, higher performing catalyst precursor compositions, catalytic compositions and catalytic processes to achieve full commercial potential for a desired reaction such as hydroformylation. The effectiveness and/or performance may be achieved in any or all of rapidity, selectivity, efficiency or stability. Other objects and advantages of the present invention will become apparent to those skilled in the art upon reference to the detailed description which hereinafter follows.
The invention provides for a hydroformylation process comprising reacting an acyclic, monoethylenically unsaturated compound with CO and H2 in the presence of a catalyst precursor composition comprising a transition metal, and at least one multidentate phosphite ligand selected from the group represented by the following formulae I, I-A or I-B, in which all like reference characters have the same meaning, except as further explicitly limited.
The invention further provides for the hydroformylation of aromatic olefins comprising reacting an acyclic aromatic olefin compound with CO and H2 in the presence of a catalyst precursor composition comprising a low-valent transition metal, and at least one multidentate phosphite ligand selected from the group represented by the following formulae I, I-A or I-B, in which all like reference characters have the same meaning, except as further explicitly limited. 
wherein X1 is a bridging group and is selected from the group consisting of: 
wherein R1, R2, R3 R4, R5, R6, R7, R8, R1xe2x80x2, and R2xe2x80x2 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, trialkylsilyl, triarylsilyl, halogen, nitrile, perfluoroalkyl, xe2x80x94SO2R11, xe2x80x94SO2NR212, acetal, ketal, dialkylamino, or diarylamino, xe2x80x94OR11, xe2x80x94CO2R11, xe2x80x94(CNR11)R11, xe2x80x94(CNOR11)R11, wherein R11 is C1 to C18 alkyl, aryl, or substituted aryl, xe2x80x94C(O)R12, xe2x80x94C(O)NR12R13, xe2x80x94Oxe2x80x94C(O)R12, xe2x80x94NR12xe2x80x94C(O)R13, wherein R12 and R13 are independently selected from the group of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl; wherein positions other than R1 through R8 on the aromatic rings may also be substituted with C1 to C18 alkyl, cycloalkyl, trialkylsilyl, triarylsilyl, halogen, nitrile, perfluoroalkyl, sulfonyl, acetal, ketal, dialkylamino, diarylamino, xe2x80x94OR11, xe2x80x94CO2R11, RCNR11, or RCNOR11,
wherein R9 and R10 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl;
wherein X2 through X5 are independently selected from the group consisting of: 
wherein Y is independently selected from the group consisting of H, aryl, CR143, (CR142)nxe2x80x94OR14, (CR142)nxe2x80x94NR15, wherein R14 is H, C1-C18 alkyl, cycloalkyl, or aryl, wherein R15 is selected from the group consisting of H, alkyl, aryl, xe2x80x94SO2R11, xe2x80x94SO2NR122, xe2x80x94COR16, wherein R16 is H, C1-C18 alkyl, cycloalkyl, aryl or perfluoroalkyl;
and Z is selected from the group consisting of (CR142)nxe2x80x94OR14 wherein n=0-3. 
In other embodiments of the invention a ligand of the structure of Formula I-A may be substituted for the ligand of Formula I, and in those embodiments an aromatic ring carbon in the ortho position to an O bonded to a P may be bonded through (Z1)n1 to another aromatic ring carbon in the ortho position to the other O bonded to the P;
wherein Z1 is independently 
and each of R17 and R18 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl, n1 is either one or zero; and wherein it is understood that n1=0 represents a bond replacing the two aromatic ring hydrogens. 
In other embodiments of the invention a ligand of the structure of Formula I-B may be substituted for the ligand of Formula I, and wherein an aromatic ring carbon in the ortho position to an O bonded to a P may be bonded through (Z1)n1 to another aromatic ring carbon in the ortho position to the other O bonded to the P;
wherein Z1 is independently 
and each of R17 and R18 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl, n1 is either one or zero; and wherein it is understood that n1=0 represents a bond replacing the two aromatic ring hydrogens.
Furthermore, in embodiments of the invention utilizing Formula I, Formula I-A or Formula I-B, either one of the Y""s may be linked with Z to form a cyclic ether.
The invention further provides for a hydroformylation process comprising reacting an acyclic, monoethylenically unsaturated compound with CO and H2 in the presence of a catalyst precursor composition comprising a transition metal, and at least one multidentate phosphite ligand selected from the group represented by the following formulae II, II-A or II-B, in which all like reference characters have the same meaning, except as further explicitly limited.
The invention further provides for the hydroformylation of aromatic olefins comprising reacting an acyclic aromatic olefin compound with CO and H2 in the presence of a catalyst precursor composition comprising a low-valent transition metal, and at least one multidentate phosphite ligand selected from the group represented by the following formulae II, II-A or II-B, in which all like reference characters have the same meaning, except as further explicitly limited. 
wherein X1 is a divalent bridging group and is selected from the group consisting of: 
wherein R1, R2, R3, R4, R5, R6, R7, R8, R1xe2x80x2, and R2xe2x80x2 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, trialkylsilyl, triarylsilyl, halogen, nitrile, perfluoroalkyl, xe2x80x94SO2R11, xe2x80x94SO2NR212, acetal, ketal, dialkylamino, or diarylamino, xe2x80x94OR11, xe2x80x94CO2R11, xe2x80x94(CNR11)R11, xe2x80x94(CNOR11)R11, wherein R11 is C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl, xe2x80x94C(O)R12, xe2x80x94C(O)NR12R13, xe2x80x94Oxe2x80x94C(O)R12, xe2x80x94NR12xe2x80x94C(O)R13, wherein R12 and R13 are independently selected from the group of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl; wherein positions other than R1 through R8 on the aromatic rings may also be substituted with C1 to C18 alkyl, cycloalkyl, trialkylsilyl, triarylsilyl, halogen, nitrile, perfluoroalkyl, sulfonyl, acetal, ketal, dialkylamino, diarylamino, xe2x80x94OR11, xe2x80x94CO2R11, RCNR11, or RCNOR11, wherein R9 and R10 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl,
wherein X2 through X5 are independently selected from the group consisting of: 
Y1 is independently selected from the group consisting of H, aryl, CR143, wherein R14 is H, C1-C18 alkyl, cycloalkyl, or aryl, (CR142)nxe2x80x94OR14, (CR142)nxe2x80x94NR15 wherein n is a number between 0 and 3, wherein R15 is selected from the group consisting of H, alkyl, cycloalkyl, aryl, xe2x80x94SO2R11, xe2x80x94SO2NR122, xe2x80x94COR16 wherein R16 is H, C1-C18 alkyl, cycloalkyl, aryl, or perfluoroalkyl;
Y2 is independently selected from the group consisting of aryl, CR143, wherein R14 is H, C1-C18 alkyl, cycloalkyl, or aryl, (CR142)nxe2x80x94OR14, (CR142)nxe2x80x94NR15 wherein n is a number between 0 and 3, wherein R15 is selected from the group consisting of H, alkyl, cycloalkyl, aryl, xe2x80x94SO2R11, xe2x80x94SO2NR122, xe2x80x94COR16 wherein R16 is H, C1-C18 alkyl, cycloalkyl, aryl, or perfluoroalkyl;
Z is selected from the group consisting of (CR142)nxe2x80x94OR14 wherein n=0-3. 
In other embodiments of the invention a ligand of the structure of Formula II-A may be substituted for the ligand of Formula II, and wherein an aromatic ring carbon in the ortho position to an O bonded to a P may be bonded through (Z1)n1 to another aromatic ring carbon in the ortho position to the other O bonded to the P;
wherein Z1 is independently 
and each R17 and R18 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl, n1 is either one or zero; and wherein it is understood that n1=0 represents a bond replacing the two aromatic ring hydrogens. 
In other embodiments of the invention a ligand of the structure of Formula II-B may be substituted for the ligand of Formula II, and an aromatic ring carbon in the ortho position to an O bonded to a P may be bonded through (Z1)n1 to another aromatic ring carbon in the ortho position to the other O bonded to the P;
wherein Z1 is independently 
and each R17 and R18 are independently selected from the group consisting of H, C1 to C18 alkyl, cycloalkyl, aryl, or substituted aryl, n1 is either one or zero; and wherein it is understood that n1=0 represents a bond replacing the two aromatic ring hydrogens.
Furthermore, in embodiments of the invention utilizing Formula II, Formula II-A or Formula II-B, either Y1 or Y2 may be linked with Z to form a cyclic ether.
The invention provides for an improved hydroformylation process which employs certain multidentate phosphite ligands. The catalyst compositions useful in the process of the invention are comprised of a multidentate phosphite ligand and a transition metal.
The divalent bridging compounds used in the ligands described in Formulae I, I-A, I-B, II, II-A, and II-B may be prepared by a variety of methods known in the art. For example, dimethyl 2,2xe2x80x2-dihydroxyl-1,1xe2x80x2-binaphthalene-3,3xe2x80x2-dicarboxylate can be prepared according to J. Am. Chem. Soc., 1954, 76, 296 or in Tetrahedron Lett., 1990, 413 and Org. Proc. Prep. International, 1991, 23, 200; 2,2xe2x80x2-ethylidenebis(4,6-dimethylphenol) can be prepared according to Bull. Chem. Soc,. Japn., 1989, 62, 3603; 3,3xe2x80x2,5,5xe2x80x2-tetramethyl-2,2xe2x80x2-biphenol can be prepared according to J. Org. Chem., 1963, 28, 1063; 2,2xe2x80x2-dihydroxy-3,3xe2x80x2-dimethoxy-5,5xe2x80x2-dimethyl-1,1xe2x80x2-biphenylene can be prepared according to Phytochemistry, 1988, 27, 3008; and 3,3xe2x80x2-dimethyl-2,2xe2x80x2-dihydroxydiphenylmethane can be prepared according to Synthesis, 1981, 2, 143. 3,3xe2x80x2,5,5xe2x80x2,6,6xe2x80x2-Hexamethyl-2,2xe2x80x2-biphenol can be prepared according to JP 85-216749.
Acetal substituted salicylaldehydes can be prepared by those skilled in the art. For example, an acetal can be prepared by refluxing a glycol with salicylaldehyde in the presence of oxalic acid catalyst. For references for preparing acetals by the acid catalyzed reaction of an aldehyde and an alcohol, see Tetrahedron, 1996, 14599; Tet. Lett., 1989, 1609; Tetrahedron, 1990, 3315. Cyclic ether substituted phenols can be prepared as described in Aust. J. Chem. 1988, 41, 69-80.
Phosphorochloridite may be prepared by a variety of methods known in the art, for example, see descriptions in Polymer, 1992, 33, 161; Inorganic Synthesis, 1966, 8, 68; U.S. Pat. No. 5,210,260; Z. Anorg. Allg. Chem., 1986, 535, 221. With ortho-substituted phenols, phosphorochloridites can be prepared in situ from PCl3 and the phenol. Also, phosphorochloridites of 1-naphthols can be prepared in situ from PCl3 and 1-naphthols in the presence of a base like triethylamine. Another process for preparing the phosphochlorodite comprises treatment of N,N-dialkyl diarylphosphoramidite with HCl. ClP(OMe)2 has been prepared in this manner, see Z. Naturforsch, 1972, 27B, 1429. Phosphorochloridites derived from substituted phenols have been prepared using this procedure as described in commonly assigned U.S. Pat. No. 5,821,378.
By contacting the thus obtained (OAr)2PCl, wherein Ar is a substituted aryl, with a divalent bridging compound, for example by the method described in U.S. Pat. No. 5,235,113, a bidentate phosphite ligand is obtained which can be used in the process according to the invention.
Bis(phosphite)ligands supported on polymer resins such as Merrifield""s resin can be prepared by similar methods, such as those described in Hetet, C. L., David, M., Carreaux, F., Carboni, B. and Sauleau, A., Tetrahedron Lett., 1997, 38, 5153-5156, and Gisin, B. F. Helv. Chim. Acta 1973, 56, 1476-1482.
The transition metal may be any transition metal capable of carrying out catalytic transformations and may additionally contain labile ligands which are either displaced during the catalytic reaction, or take an active part in the catalytic transformation. Any of the transition metals may be considered in this regard. The preferred metals are those comprising group VIII of the Periodic Table. The preferred metals for hydroformylation are rhodium, cobalt, iridium, ruthenium, palladium and platinum.
Group VIII compounds suitable for hydroformylation, can be prepared or generated according to techniques well known in the art, as described, for example, WO 95 30680, U.S. Pat. No. 3,907,847, and J. Amer. Chem. Soc., 1993, 115, 2066. Examples of suitable Group VIII metals are ruthenium, rhodium, and iridium. Suitable Group VIII metal compounds are hydrides, halides, organic acid salts, acetylacetonates, inorganic acid salts, oxides, carbonyl compounds and amine compounds of these metals. Examples of suitable Group VIII metal compounds are, for example, Ru3(CO)12, Ru(NO3)2, RuCl3(Ph3P)3, Ru(acac)3, Ir4(CO)12, IrSO4, RhCl3, Rh(NO3)3, Rh(OAc)3, Rh2O3, Rh(acac)(CO)2, [Rh(OAc)(COD)]2, Rh4(CO)12, Rh6(CO)16, RhH(CO)(Ph3P)3, [Rh(OAc)(CO)2]2, and [RhCl(COD)]2 (wherein xe2x80x9cacacxe2x80x9d is an acetylacetonate group; xe2x80x9cOAcxe2x80x9d is an acetyl group; xe2x80x9cCODxe2x80x9d is 1,5-cyclooctadiene; and xe2x80x9cPhxe2x80x9d is a phenyl group). However, it should be noted that the Group VIII metal compounds are not necessarily limited to the above listed compounds. The Group VIII metal is preferably rhodium. Rhodium compounds that contain ligands which can be displaced by the multidentate phosphites are a preferred source of rhodium. Examples of such preferred rhodium compounds are Rh(CO)2 (acetylacetonate), Rh(CO)2(C4H9COCHCO-t-C4H9), Rh2O3, Rh4(CO)12, Rh6(CO)16, Rh(O2CCH3)2, and Rh(2-ethylhexanoate). Rhodium supported on carbon may also be used in this respect.
The present invention also provides a process for hydroformylation, comprising reacting a monoethylenically unsaturated compound with a source of CO and H2 in the presence of a catalyst precursor composition comprising a transition metal selected from the group of Co, Rh, Ru, Ir, Pd, and Pt, and at least one multidentate phosphite ligand selected from the group represented by Formula I, I-A, I-B, II, II-A, or II-B as described above.
Representative ethylenically unsaturated compounds which are useful in the process of this invention are shown in Formulae III, V or VII, and the corresponding terminal aldehyde compounds produced are illustrated by Formulae IV, VI or VIII, respectively, wherein like reference characters have same meaning. 
wherein
R19 is H, CN, CO2R20, or perfluoroalkyl;
y is an integer of 0 to 12;
x is an integer of 0 to 12 when R19 is H, CHO, CO2R20 or perfluoroalkyl;
x is an integer of 1 to 12 when R19 is CN; and
R20 is C1 to C12 alkyl, or aryl. 
R21 is an alkyl, aryl, aralkyl, alkaryl, or fused aromatic group of up to 20 carbon atoms; R21 may further be branched or linear; R21 may also contain heteroatoms such as O, N, and F.
The nonconjugated, aliphatic, monoolefinically unsaturated starting materials useful in this invention include unsaturated organic compounds containing from 2 to approximately 30 carbon atoms. Suitable unsaturated compounds include unsubstituted hydrocarbons as well as hydrocarbons substituted with groups which do not attack the catalyst, such as cyano. These unsaturated compounds include monoethylenically unsaturated compounds containing from 2 to 30 carbons such as ethylene, propylene, 1-butene, 2-pentene, 2-hexene, etc.; nonconjugated diethylenically unsaturated compounds such as allene; ethylenically unsaturated compounds having perfluoroalkyl substituents such as, for example, CzF2z+1, where z is an integer of up to 20; and substituted compounds such as allyl alcohol, 3-pentenenitrile, 4-pentenenitrile, methyl-3-pentenoate, methyl-4-pentenoate, 3-pentenal, 4-pentenal, and functional derivatives, such as acetals, imines, and hydrazones derived from 3- or 4-pentenal;. As used herein, the term xe2x80x9cpentenenitrilexe2x80x9d is intended to be identical with xe2x80x9ccyanobutenexe2x80x9d. The monoolefins propylene, 1-butene, 2-butene, 3-pentenenitrile, and 4-pentenenitrile are especially preferred. As a practical matter, when the nonconjugated aliphatic monoethylenically unsaturated compounds are used in accordance with this invention, up to about 10% by weight of the monoethylenically unsaturated compound may be present in the form of a conjugated isomer, which itself may undergo hydroformylation.
Preferred are nonconjugated linear alkenes, nonconjugated linear alkenenitriles, nonconjugated alkyl pentenoates, nonconjugated pentenals, acetal derivatives of pentenals, and perfluoroalkyl ethylenes. Most preferred substrates include methyl-3-pentenoate, 3-pentenal (3-pentenealdehyde), 3- and 4-pentenenitrile and CzF2z+1CHxe2x95x90CH2 (where z is 1 to 12).
The preferred products are terminal alkanealdehydes, linear aliphatic aldehyde nitriles, and 3-(perfluoroalkyl)propionaldehyde. Most preferred products are n-butyraldehyde, 2-phenylpropionaldehyde, and 5-cyano-valeraldehyde.
The reaction conditions of the hydroformylation process according to this invention are in general the same as used in a conventional process, described, for example, in U.S. Pat. No. 4,769,498, which is incorporated herein by reference and will be dependent on the particular starting ethylenically unsaturated organic compound. For example, the temperature can be from room temperature to 200xc2x0 C., preferably from 50-120xc2x0 C. The pressure may vary from atmospheric pressure to 20 MPa, preferably from 0.15 to 10 MPa and more preferably from 0.2 to 1 MPa. The pressure is, as a rule, equal to the combined hydrogen and carbon monoxide partial pressure. Extra inert gases may however be present. The molar ratio of hydrogen to carbon monoxide is generally between 10 to 1 and 1 to 10, preferably between 6 to 1 and most preferably 1 to 2.
The amount of rhodium compound is not specially limited, but is optionally selected so that favorable results can be obtained with respect to catalyst activity and economy. In general, the concentration of rhodium in the reaction medium is between 10 and 10,000 ppm and more preferably between 50-500 ppm, calculated as the free metal.
The molar ratio of multidentate phosphorus ligand to rhodium is not specially limited, but is optionally selected so that favorable results can be obtained with respect to catalyst activity, aldehyde selectivity, and process economy. This ratio generally is from about 0.5 to 100 and preferably from 1 to 10 (moles of ligand to moles of metal).
The choice of solvent is not critical provided the solvent is not detrimental to catalyst, reactant and product. The solvent may be a mixture of reactants, such as the starting unsaturated compound, the aldehyde product and/or by-products. Suitable solvents include saturated hydrocarbons such as kerosene, mineral oil or cyclohexane, ethers such as diphenyl ether, tetrahydrofuran or a polyglycol, ketones such as methyl ethyl ketone and cyclohexanone, nitrites such as methylglutaronitrile, valeronitrile, and benzonitrile, aromatics such as toluene, benzene and xylene, esters such as methyl valerate and caprolactone, dimethylformamide, and sulfones such as tetramethylenesulfone. The reaction may also be conducted with reactants and products in the gas phase.
Preferably, when a liquid reaction medium is used, the reaction mixture is agitated, such as by stirring or shaking.
Other catalysts useful in the practice of the present invention consist of the class of polymer-supported bis(phosphorus) ligands in combination with transition metal compounds, the metals of which are, for example, rhodium, ruthenium, cobalt, palladium or platinum. Alternatively, useful catalysts can be prepared from a combination of bis(phosphorus) ligand and a suitable transition metal complex, such as Rh(acetonylacetonate)(CO)2 or Rh4(CO)12, dispersed on a suitable support, such as silica, alumina, carbon or a polymeric material.
The hydroformylation process according to the invention can be performed as described below:
The preferred temperature range is from about 50xc2x0 C. to about 180xc2x0 C., most preferably from about 90xc2x0 C. to 110xc2x0 C. The temperature must be chosen so as to maintain all of the reactants and products in the vapor phase, but low enough to prevent deterioration of the catalyst. The particular preferred temperature depends to some extent on the catalyst being used, the olefinic compound being used, and the desired reaction rate. The operating pressure is not particularly critical and can conveniently from about 1-10 atmospheres (101.3 to 1013 kPa). The pressure and temperature combination must be chosen so as to maintain reactants and products in the vapor phase.
The invention will now be illustrated by the following non-limiting examples of certain embodiments thereof, wherein all parts, proportions, and percentages are by weight, unless otherwise indicated.
The following definitions are applicable wherever the defined terms appear in this specification:
The term xe2x80x9chydrocarbylxe2x80x9d designates a hydrocarbon molecule from which one hydrogen atom has been removed. Such molecules can contain single, double or triple bonds.
M3P: methyl 3-pentenoate
COD: 1,5-cyclooctadiene
Et3N: triethylamine
PCl3: phosphorus trichloride
THF: tetrahydrofuran
3PN; 3-pentenenitrile
2PN: 2-pentenenitrile
4PN: 4-pentenenitrile
2M3: 2-methyl-3-butenenitrile
VN: valeronitrile
3FVN: 3-formylvaleronitrile
4FVN: 4-formylvaleronitrile
5FVN: 5-formylvaleronitrile
BD: 1,3-butadiene
c=cis
t=trans
L/M=ligand/metal
An example of the protocol used to calculate conversion, linearity, and selectivity for a hydroformylation reaction follows:.
Total=c2PN+VN+t2PN+t3PN+4PN+c3PN+4FVN+3FVN+5FVN
Products=c2PN+VN+t2PN+4FVN+3FVN+5FVN
Accounting=Total/amount 3PN added initially
Conversion=Products/Total
Linearity=5FVN/(5FVN+4FVN+3FVN)
Selectivity=5FVN/Products